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Using a modified dynamic Monte Carlo renormalization group method, the two- dimensional kinetic Ising model is studied, and the dynamic critical exponent is obtained. The critical temperature of phase transition can be obtained by the renormalization method for the correlation function. In the method we used, the correlation function is replaced with the absolute value of the magnetization, and it is found that the evolution of the absolute value of the magnetization over time satisfies the power-law form. It is found that the value of the dynamic critical exponent tends to be a stable value in the form of a power-law function as the scale of the system increases. The dynamic critical exponent obtained is z ≃ 2 . 15 . When the modified dynamic Monte Carlo renormalization group method is applied to the two-dimensional Glauber model, the obtained dynamic critical exponent is z ≃ 2 . 25 .

The fluctuation behaviors of a gene transcriptional regulatory system subjected to the cross-correlated noises are investigated. Based on the approximate Fokker–Planck Equation, the analytic expressions of the associate relaxation time and the correlation function of a gene transcriptional regulatory system are obtained by means of projection operator method. The results show that the noise parameters exhibit different effects on the fluctuation behaviors of this system, and can produce the critical behaviors in the relaxation time as functions of the multiplicative noise intensity D , the additive noise intensity α and the cross-correlated noise intensity λ . That is, the relaxation time decreases below the critical value of λ , and above the critical value of D and α . The rate of fluctuation decay of concentration state of TF-A is speeded up, the stability of this system is enhanced. However, above the critical value of λ , and below the critical values of D and α , the relaxation time first increases, reaches a maximum, and then decreases. The rate of fluctuation decay of concentration state of TF-A is slowed down firstly, and then, is enhanced. On the other hand, the effects of noise parameters on the correlation function show that λ and α weaken the related activity between two states at different time, and enhances the stability of the system in the steady state. In contrast, D enhances the related activity between two states at different time, and weakens the stability. The numerical results are in basic agreement with the theoretical predictions.

Long-range bidirectional transport depends on the collective motion of interacting particles and associations in the entrance and exit of several transport mediums. Motivated by these observations we analyze a bidirectional framework with a narrow entrance to explore the fundamental role of interactions on the system dynamics. The complex phenomena such as phase transitions and spontaneous symmetry breaking for variant attractive and repulsive interactions are examined within the structure of the mean-field theory and computer simulations. We examined the control of interactions on the symmetry breaking structure, in particular, its appearance/disappearance. It is observed that for a certain range of attraction and repulsion rates, the system exhibits both symmetric and asymmetric behavior, while for their higher values asymmetry disappears. The critical values of interaction strength, beyond which symmetrical and asymmetrical phases appear and disappear are identified and the phase transition lines for these phases have been obtained theoretically. Interestingly, it is found that the region of asymmetric phases exhibits non-monotonic behavior with increasing attractive interactions. The finite size effect and symmetry-breaking phenomenon based on the density distribution functions from Monte Carlo simulations have also been examined. Finally, the impact of correlation strength on the system behavior has been analyzed using two-point correlation function based on simulations.

We study the evolution of the squeezing-enhanced vacuum state (SEVS) in the amplitude dissipative channel by using the two-mode entangled state in the Fock space and Kraus operator. The explicit formulation of the output state is also given. It is found that the output state does not exhibit sub-Poissonian behavior for the nonnegative value of the Mandel’s Q-parameters in a wide range of values of squeezing parameter and dissipation factor. It is interesting to see that second-order correlation function is independent of the dissipation factor. However, the photon-number distribution of the output quantum state shows remarkable oscillations with respect to the dissipation factor. The shape of Wigner function and the degree of squeezing show that the initial SEVS is dissipated by the amplitude dissipative channel.

While the usual goal in Monte Carlo (MC) simulations of Ising models is the efficient generation of spin configurations with Boltzmann probabilities, the inverse problem is to determine the coupling constants from a given set of spin configurations. Most recent work has been limited to local magnetic fields and pair-wise interactions. We have extended solutions to multi-spin interactions, using correlation function matching (CFM). A more serious limitation of previous work has been the uncertainty of whether a chosen set of interactions is capable of faithfully representing real data. We show how our confirmation testing method uses an additional MC simulation to detect significant interactions that might be missing in the assumed representation of the data., 5 pages, 3 figures

We study a stochastic process defined by the interaction strength for the return to the mean and a stochastic term proportional to the magnitude of the variable. Its steady-state distribution is the Inverse Gamma distribution, whose power-law tail exponent is determined by the ratio of the interaction strength to stochasticity. Its time-dependence is characterized by a set of discrete times describing relaxation of respective cumulants to their steady-state values. We show that as the progressively lower cumulants diverge with the increase of stochasticity, so do their relaxation times. We analytically evaluate the correlation function and show that it is determined by the longest of these times, namely the inverse interaction strength, which is also the relaxation time of the mean. We also investigate relaxation of the entire distribution to the steady state and the distribution of relaxation times, which we argue to be Inverse Gaussian.

From the view of intrinsic noise in semiconductors, the model of charge-particles transport in one-dimensional semiconductors described by a generalized Langevin equation (GLE) driven by a intrinsic fractional Gaussian noise is proposed in this paper. The analytical expression of the average charged particle velocity, the differential mobility, the conductivity of charge-particles, the two-time correlation function of the velocity fluctuation and the power spectral of total current density fluctuation have been derived. Furthermore, the model of motion for the charge-particle subjected to an electric field and a magnetic field governed by GLE is introduced. The expressions of mean values and variances of charged particle velocity, Fokker–Planck equation of charge-particle motion, the asymptotic behaviors of the relaxation functions have been obtained. Under the Hall effect, the Hall angle, the Hall coefficient, as well as the electrical resistivity also have been studied.

a b s t r a c t We review equilibrium properties for the dynamics of a single particle evolving in a visco- elastic medium under the effect of hydrodynamic backflow which includes added mass and Basset force. Arbitrary equilibrium forces acting upon the particle are also included. We discuss the derivation of the explicit expression for the thermal noise correlation function that is consistent with the fluctuation-dissipation theorem. We rely on general time- reversal arguments that apply irrespective of the external potential acting on the particle, but also allow one to retrieve existing results derived for free particles and particles in a harmonic trap. Some consequences for the analysis and interpretation of single-particle tracking experiments are briefly discussed.

The Lieb–Schupp inequality is the inequality between ground state energies of certain antiferromagnetic Heisenberg spin systems. In our paper, the numerical value of energy difference given by Lieb–Schupp inequality has been tested for spin systems in various geometries: chains, ladders and quasi-two-dimensional lattices. It turned out that this energy difference was strongly dependent on the class of the system. The relation between this difference and a fall-off of a correlation function has been empirically found and formulated as a conjecture.

We propose a simple analytical expression of the direct correlation function for the square-shoulder and square-well fluids. Our approximation is based on an ansatz for the direct correlation function of a modified soft-core fluid, whose parameters are adjusted by fitting the data obtained from Monte Carlo computer simulations. Moreover, it is complemented with a Wertheim-like parametrization to reproduce correctly the direct correlation inside the hard-core. We demonstrate that this approach is in quantitative agreement with the numerical solution of the Ornstein–Zernike equation within the Percus–Yevick approximation. We also show that our results are accurate in a large regime of densities for different interaction ranges and potential strengths. Therefore, this opens up the possibility of introducing the square-shoulder or the square-well potentials as new reference systems in advanced theoretical approximations.

We show how to construct the optimum superstatistical dynamical model for a given experimentally measured time series. For this purpose we generalise the superstatistics concept and study a Langevin equation with a memory kernel whose parameters fluctuate on a large time scale. It is shown how to construct a synthetic dynamical model with the same invariant density and correlation function as the experimental data. As a main example we apply our method to velocity time series measured in high-Reynolds number turbulent Taylor-Couette flow, but the method can be applied to many other complex systems in a similar way., 11 pages, 4 figures

The height–height correlations of the surface growth for equilibrium and nonequilibrium restricted solid-on-solid (RSOS) model were investigated on randomly diluted lattices, i.e., on infinite percolation networks. It was found that the correlation function calculated over the chemical distances reflected the dynamics better than that calculated over the geometrical distances. For the equilibrium growth on a critical percolation network, the correlation function for the evolution time t ≫ 1 yielded a power-law behavior with the power ζ ′ , associated with the roughness exponent ζ via the relation ζ = ζ ′ d f / d l , with d f and d l being, respectively, the fractal dimension and the chemical dimension of the substrate. For the nonequilibrium growth, on the other hand, the correlation functions did not yield power-law behaviors for the concentration of diluted sites x less than or equal to the critical concentration x c .

Self-diffusion in multi-component glass-forming systems including fragile and strong glasses is studied from a unified viewpoint. A simple analytic form of long-time self-diffusion coefficient D S L is proposed. The equations for the mean-square displacements recently derived for two types of systems, (S) suspensions of colloids and (M) molecular systems, from a first principle by employing the Tokuyama–Mori projection-operator method are used to define D S L in each type formally, both of which are uniquely determined by the correlation function of the fluctuating forces. Analyses of the correlation functions in two types in terms of many-body interactions thus lead in type (M) to D S L ( λ ) ≃ κ − 1 ( λ c / λ ) ( 1 − λ / λ c ) 2 , where λ is a control parameter, such as an inverse temperature and a volume fraction. Here κ is simply written in terms of the potential parameters and λ c an adjustable parameter to be determined. The predictions for λ dependence of D S L in multi-component glass-forming systems are in excellent agreement with available experimental data and simulation results in equilibrium states.

Density functional theory is used to study the structure of a one dimensional fluid model of hard-ellipse molecules with their axes freely rotating in a plane, confined between hard walls. A simple Hypernetted chain (HNC) approximation is used for the density functional of the fluid and the integral equation for the density is obtained from the grand potential. The only required input is the direct correlation function of the one dimensional hard-ellipse fluid. For this model, the pressure, sum rule and the density at the walls are obtained. The Percus Yevick (PY), for lower density, and HNC, for higher density, integral equations are also solved to obtain the direct correlation function of hard-ellipse model introduced here. We obtain the average density at the wall as well as the radial density profile. We compare these with Monte Carlo simulations of the same model and find reasonable agreement.

The high-temperature expansions of the spin-spin correlation function of the two-dimensional classical X Y (planar rotator) model are extended by two terms, from order 24 through order 26, in the case of the square lattice, and by five terms, from order 15 through order 20, in the case of the triangular lattice. The data are analyzed to improve the current estimates of the critical parameters of the models. We determine β c = 0.5599 ( 7 ) and σ = 0.499 ( 5 ) in the case of the square lattice. For the triangular lattice case, we estimate β c = 0.3412 ( 4 ) and σ = 0.500 ( 5 ) .

The effect of a uniform field H on the dynamics of the Ising spin glass FexZn1-xF2, x=0.25, is studied through Monte Carlo simulations. The correlation function data are consistent with the droplets picture, with a single scaling variable t/tw, where tw is the waiting time under H, activation over logarithmic energy barriers near the percolation threshold, xp=0.24, and considerable change of the glassy phase for intermediate and high H.

The Brownian motion of a particle in a double-well potential is considered and the position correlation function (excluding inertial effects) for the potential V ( x )= ax 2 /2+ bx 4 /4 is evaluated first by averaging the governing Langevin equation over its realizations. The exact solution is then obtained via matrix continued fractions by using a representation, which symmetrizes the recurrence relations for the observables generated by the averaging procedure leading to convergence of these recurrence relations unlike the previous approaches to the problem. A reliable approximate solution based on the exponential separation of the time scales of the fast intrawell and low overbarrier relaxation processes associated with the bistable potential is also given. It is shown that a knowledge of the three characteristic relaxation times (the integral, effective and the longest relaxation times) of the position correlation function allows one to accurately predict the relaxation behavior of the system in the overdamped limit for all time scales of interest.

We review a recently devised Monte Carlo simulation method for the direct study of quasi-stationary properties of stochastic processes with an absorbing state. The method is used to determine the static correlation function and the interparticle gap-length distribution in the critical one-dimensional contact process. We also find evidence for power-law decay of the interparticle distance distribution in the two-particle subspace., Comment: 9 pages, 4 figures

The relaxation time T c of the intensity correlation function is investigated in a single-mode dye laser system driven by cross-correlated additive and multiplicative white noises. The expression for T c is obtained by using the projector–operator method. And then the effects of correlation intensity between noises λ and correlation time between noises τ on T c are studied. Numerical results show that the correlation intensity λ speeds up the intensity fluctuation decay of laser slightly above threshold in the presence of nonzero τ . Meanwhile, when λ > 0 , τ suppresses the intensity fluctuation of laser. But when λ > 0 , τ enhances the intensity fluctuation of laser. Moreover, the effects of λ and τ on the intensity fluctuation also depend on the noise intensity ratio R and net gain coefficient a 0 .

The topological interaction method proposed by Suzuki is applied to the transverse Ising chain and XY chain in order to study the behaviour of the boundary–boundary correlations. The correlation function 〈 σ 1 x σ N x 〉 for the thermodynamic limit is derived by this method as a function of the topological interaction parameter J 2 for finite temperatures. This analysis of the correlation function clarifies the emergence of the long-range order as temperature goes to zero. At zero temperature, a more general spin chain can be analysed analytically for N → ∞ and numerically for finite N to obtain the following results. The correlation function 〈 σ 1 x σ N x 〉 shows various kinds of behaviour, namely, (a) monotonic, (b) non-monotonic or (c) globally non-monotonic with small oscillation, with respect to the system-size N, in different regions of the parameters. The function 〈 σ 1 y σ N y 〉 shows also the above behaviour (a), or shows (d) globally monotonic decay with small oscillation.

We show that the general procedure developed by Fox and Uhlenbeck (Phys. Fluids 3 (1970) 1893) may be employed to describe the hydrodynamic fluctuations of a thermotropic nematic liquid crystal in equilibrium and steady states. We calculate explicitly the matrix of correlation functions for the transverse variables of a nematic film confined between two horizontal plates and subjected to a constant pressure gradient. We find that the light scattering spectrum and the intensity of the Rayleigh line are calculated from the orientation correlation function in equilibrium to first order in the pressure gradient. The shape and intensity of these lines deviate from their equilibrium values by amounts proportional to the imposed gradient, leading to an asymmetry in their height and intensity. It is shown that these effects may as large as 94.3% for a value of ∣ ∇ p ∣ = 2.64 × 10 - 2 atm / cm of the pressure gradient, suggesting that this effect might be observable.

The object of this work is to calculate the effective dielectric constant tensor of a warm plasma made of non point-like ions in an electron gas whose screening length is much larger than the inter-ionic and inter-electronic distances. In this disordered medium, a proper treatment of the screening effects is proposed, and developed in the case of an ionic electromagnetic response described through an ad hoc dielectric constant. Here the latter is extracted from the ion RPA response. In the linear regime in ion density, one obtains a new mixing law for the dielectric constant. It's transverse part is compared with the Maxwell Garnett mixing law. In this paper one also gives the basis for its companion, where the complete calculation of the ionic scattering matrix will allow one to go further in ion density using a liquid-like 2-point correlation function to describe the ionic disorder.

The effects of correlations between additive and multiplicative noises on the state variable correlation function of a bistable system driven by cross-correlated noises were studied. Applying an approximate Fokker–Planck equation to the system, the analytic expression for the state variable correlation function of the system is derived by projection operator method. From numerical computations we find that the normalized correlation function C ( s ) decreases exponentially as the decay time s increases and decreases with increasing cross-correlated strength λ , however C ( s ) increases with increasing cross-correlated time τ . λ and τ play opposing roles in the C , i.e., λ enhances the rate of fluctuation decay of dynamical variable and the τ slows down the rate of fluctuation decay of dynamical variable.

The long time coarse grain of the observables often shows the large deviation statistics. A reason for this is that the long time coarse grained observables lose their correlations or memories. The establishment of the large deviation statistics leads to the statistical mechanics. In this paper, we show examples to prove that the probability distribution functions are well-defined for the nonlinear dynamical systems as a result of the coarse grained time being longer than the correlation time of the systems.

We compute the correlation function in the equilibrium version of R\'enyi's {\sl parking problem}. The correlation length is found to diverge as $2^{-1}\pi^{-2}(1-\rho)^{-2}$ when $\rho\nearrow1$ (maximum density) and as $\pi^{-2}(2\rho-1)^{-2}$ when $\rho\searrow1/2$ (minimum density)., Comment: 9 pages, 1 figure

The morphological concept of parallel surfaces in combination with curvature measures known from integral geometry are used to characterise and model complex spatial structures beyond the two-point correlation function and to predict, for instance, percolation thresholds in porous media. Applied to liquid interfaces one finds a reduction of the surface tension at microscopic scales in good agreement with X-ray scattering experiments.

We analyse the relationship between dynamics and configuration space structure of Ising spin glass systems. The exact knowledge of the structure of the low--energy landscape is used to study the relaxation of the system by random walk in the configuration space. The influence of the size of the valleys, clusters and energy barriers and the connectivity between them on the spin correlation function is shown., 6 pages,4 figures, APCTP International Symposium on Slow Dynamical Processes in Nature, Seoul 2001

The system described by the Kuramoto–Sivashinsky equation (SKSE) is shown to have a short- and a long-time regimes. The probability distribution function (PDF) for the absolute value of the solution is subjected to different scaling laws in the two time regimes. The local expansion rate (LER) and its two-time correlation function are calculated. The time regime where the correlation for the LER remains is shorter than the one for the absolute value of the solution for the SKSE. The fluctuation in the LER becomes small as the damping constant is increased. The PDF for the LER is also given in this paper.

The fractal dimension (FD) is a widely used magnitude having a basic formulation in terms of the Hausdorff measure. However, there are a lot of practical definitions mostly used to compute the FD of a given system not yet having a mathematically rigorous approach. In this paper, we analyze these alternative FDs and present a mathematical formalism for all of them obtaining practical expressions that can be used to compute each FD so far described. The conditions for applying these expressions are also analyzed. Finally, we have applied all the definitions to compute the FD of fractal aggregates formed at the air–liquid interface.

The state vector is defined for the phase turbulence described by the Kuramoto–Sivashinsky equation. Then the two-time correlation function (TTCF) for the state vector is calculated numerically. In the case when the damping constant is zero, the TTCF decays like Lorentzian. The TTCF changes its shape as we increase the value of the damping constant from zero. In addition, the local expansion rate is calculated and it is shown that the local expansion rate fluctuates around at zero.

We investigate, through the damage spreading method, the correlation length associated with the two-point correlation function between damage fluctuations, and the damage susceptibility of the square-lattice three-state Potts ferromagnet. We find that both quantities tend to diverge at the damage transition. These results can be interpreted as a first evidence of a possible fluctuation–dissipation-like relation between damage quantities in this model.

The universal finite-size correction to the free energy of a two-dimensional Coulomb system is checked in the special case of a one-component plasma on a sphere. The correction is related to the known second moment of the short-range part of the direct correlation function for a planar system., 3 pages, 1 figure, to appear in Physica A

Properties of semi-infinite (S=1) Heisenberg ferromagnet with biquadratic exchange were studied in terms of surface exchange (e=IS/I) and biquadratic coupling (a). It was shown that a strict correlation exists, depending on e, between the type of surface spin waves (acoustic or optical) and the mean-field (MF) critical temperature, bulk (Tc) and surface TcS>Tc (for ). Within the framework of the Landau–Ginsburg theory for semi-infinite simple cubic ferromagnet, a detailed study is presented of the critical behaviour of the system, in particular in the vicinity of the tricritical point which is the consequence of the biquadratic interaction. It is shown that tricritical exponents satisfy exactly the scaling relations for d=3. The analysis of the spin–spin correlation function within the framework of the same theory, shows that there occurs the critical magnetic scattering of low-energy electrons (LEED) from the surface in the case , when the ordering temperature TcS is approached from above (from paramagnetic phase). In the opposite case, , there occurs no surface critical scattering. It was also shown that in the vicinity of the tricritical point, the biquadratic interaction increases the range of validity of the MF approximation.

A kinetic model of a reaction–diffusion system by which fluctuation around a nonequilibrium steady state can be analyzed without resorting to a local equilibrium assumption is discussed. The spatial correlation function of concentration fluctuations is analytically calculated, and it is shown that (i) the result is consistent with the previous studies for sufficiently slow chemical reactions, and (ii) how the correlation function is modified when chemical reactions are fast.

Two-dimensional crystal is tested in the system of several millimeter size polystyrene spheres. Large numbers of same size spheres are triboelectrically charged through rubbing on the substrate plate. Therefore, one can observe the two-dimensional system without the help of any instrument and can easily micro-control the condition of two-dimensional system. The Fourier transform spectra, the pair distribution and the bond-orientational correlation function data show that the system is in near hexatic phase after fully charged, which is predicted by the KTHNY theory.

In Tsallis’ generalized statistical mechanics, correlation is induced by nonextensivity even if the microscopic degrees of freedom are dynamically independent. Here, using the classical ideal gas model, the generalized variance, covariance and correlation coefficient regarding the particle energies are calculated and their properties discussed. It is shown that the correlation is suppressed for a large number of particles. This demonstrates the validity of the independent particle picture for a dense gas rather than for a dilute gas. It is also found that, in the thermodynamic limit, the correlation again vanishes and the generalized variance exhibits a power-law behavior with respect to the particle number density. Relevance of these results to the zeroth law of thermodynamics in nonextensive statistical mechanics is pointed out.

We dene a generic correlation function that quanties the spatial correlation of single-particle displacements in liquids and amorphous systems. We evaluate this function using computer simulations of an equilibrium glass-forming liquid, and show that the displacements of particles are spatially correlated over a range that grows with decreasing temperature as the glass transition is approached. c 1998 Elsevier Science B.V. All rights reserved.

A correlation between the logarithm of the secondary β-relaxation time, log[τβ(Tg)], and the Kohlrausch exponent, (1−n), of the primary α-relaxation correlation function exp[−(t/τα)1−n] has been found in glass-forming materials in general. I was guided to this finding by the coupling model based on the similarity of some secondary β-relaxation to the primitive α-relaxation of the model. The logarithm of the primitive α-relaxation time at Tg,log[τ0(Tg)], calculated according to the coupling model from the observed α-relaxation at Tg, is exactly correlated with the Kohlrausch exponent. A similar, although inexact, correlation between log[τβ(Tg)] and (1−n) is thus expected and found. Furthermore, the experimental values of τβ(Tg) are remarkably close in order of magnitude to τ0(Tg) for many glass-formers as anticipated.

Continuing our work [1] , where a explicit formula for the two-point functions of the two-dimensional Z-invariant Ising model were found. I obtain here different results for the higher correlation functions and several consistency checks are done.

We develop a transfer matrix method to compute exactly the spin–spin correlation functions for Bethe lattice Ising model and Blume–Emery–Griffiths (BEG) model in the external magnetic field h and for any temperature T. The correlation length ξ(T,h) obtained from the spin–spin correlation function shows interesting scaling and divergent behavior as h→0 and T approaches the critical temperature Tc.

The Domany–Kinzel cellular automaton is a simple and yet very rich model to study phase transitions in nonequilibrium systems. This model exhibits three characteristic phases: frozen, active and chaotic. In this paper we discuss the behavior of the equal-time two-point correlation functions and that of the associated correlation lengths as one crosses the phase boundary both for the frozen–active and active–chaotic transitions. We have investigated in detail how the correlation lengths diverge as one approaches the phase boundary from both sides. The divergence of the correlation length coupled with the previous studies on the divergence of the susceptibility, suggests that the fluctuation–dissipation theorem holds true in the Domany–Kinzel cellular automaton model. Time dependence of the correlation functions is also discussed.

19 pages, 6 figures.-- PACS nrs.: 05.40.+j; 05.70.Ln; 68.35.Fx. In this paper we study kinetically rough surfaces which display anomalous scaling in their local properties such as roughness, or height-height correlation function. By studying the power spectrum of the surface and its relation to the height-height correlation, we distinguish two independent causes for anomalous scaling. One is super-roughening (global roughness exponent larger than or equal to one), even if the spectrum behaves nonanamalously. Another cause is what we term an intrinsically anomalous spectrum, in whose scaling an independent exponent exists, which induces different scaling properties for small and large length scales (that is, the surface is not self-affine). In this case, the surface does not need to be super-rough in order to display anomalous scaling. In both cases, we show how to extract the independent exponents and scaling relations from the correlation functions, and we illustrate our analysis with two exactly solvable examples. One is the simplest linear equation for molecular beam epitaxy, well known to display anomalous scaling due to super-roughening, The second example is a random diffusion equation, which features anomalous scaling independent of the value of the global roughness exponent below or above one. J.M.L. acknowledges the Postdoctoral Program of Universidad de Cantabria for support at Instituto de Física de cantabria where most of this work has been made. This work has been supported by DGICyT of the Spanish Government under Project Nr. PB93-0054-C02-02. Publicado

We study the spin-spin correlation function in or near the T=0 ground state of the antiferromagnetic Ising model on a triangular lattice. At zero temperature its modulation on the sublattices gives rise to two Bragg peaks in the structure factor, and a known expression for the algebraic decay of correlations enables us to examine the form of the diffusive scattering. We do so by means of a comparison between exact results and data calculated using standard Monte Carlo techniques. At non-zero temperatures the finite correlation length alters this form, and we account for the change by proposing a generalisation of the zero temperature pair correlation function. The size dependence of our simulation data is investigated through a novel finite-size scaling analysis where t = exp(-2/T) is used as the temperature parameter., Comment: 14 pages (RevTeX) and 11 ps-figures. Accepted for publication in Physica A

The scattering of coherent X-rays from dynamically evolving systems is currently becoming experimentally feasible. The scattered beam produces a pattern of bright and dark speckles, which fluctuate almost independently in time and can be used to study the dynamics of the system. Here we report large-scale computer simulations of the speckle dynamics for a phase ordering system, using a two-dimensional model quenched through an order--disorder transition into the two-phase regime. The intensity at each wave vector ${\bf k}$ is found to be an exponentially distributed random variable. The scaling hypothesis is extended to the two-time correlation function of the scattering intensity at a given wave vector, $Corr({\bf k};t_1,t_2)$. The characteristic decay time difference for the correlation function, $|t_1 - t_2|_c$, is found to scale as $k|t_1 + t_2|^{1/2}$., Comment: 11 Pages, RevTex, 6 PostScript Figures Accepted to Physica A

We re-examine a two-dimensional forest-fire model via Monte-Carlo simulations and show the existence of two length scales with different critical exponents associated with clusters and with the usual two-point correlation function of trees. We check resp. improve previously obtained values for other critical exponents and perform a first investigation of the critical behaviour of the slowest relaxational mode. We also investigate the possibility of describing the critical point in terms of a distribution of the global density. We find that some qualitative features such as a temporal oscillation and a power law of the cluster-size distribution can nicely be obtained from such a model that discards the spatial structure., 20 pages plain TeX, 7 figures included using psfig.sty, PostScript for the complete paper also available at http://www.physik.fu-berlin.de/~ag-peschel/papers/forest2d.ps.gz , extra software at http://www.physik.fu-berlin.de/~ag-peschel/software/forest2d.html ; main change: inclusion of further data in the determination of nu_T in Section 2.1 + some small changes; final version to appear in Physica A

We propose a new method to determine the multi-affine fractal exponents based on a generalization of the roughness concept. For synthetic multi-affine fractal profiles with exactly known exponents, we show that the results obtained in this method are more accurate than the results obtained with the height-height correlation function method. Also in the present method, scaling is observed using profiles with a number of points more than one order mangnitude smaller.

Small-angle neutron scattering (SANS) measurements are made on a three-component isometric (equal volume fractions of water and oil) microemulsion system, composed of AOT/water (0.4% NaCl)/D-octane, in the one-phase channel near the three-phase region at and around the hydrophile-lipophile balance temperature. A previous SANS contrast variation experiment indicated that the microstructure of this type of isometric microemulsion is bicontinuous in water and oil with the surfactant film at the interface having a zero mean curvature. We analyze SANS data taken with an oil-water contrast in terms of a modified Berk's random wave model. We choose a spectral function which is an inverse sixth-order polynomial, with three parameters a, b and c, as introduced by Lee and Chen earlier. This three-parameter spectral function is then used in conjunction with Cahn's clipping scheme to obtain the Debye correlation function appropriate for the microemulsion system. The model analysis results in good agreement with the intensity data in an absolute scale. We then use the three parameters so obtained to calculate the average Gaussian curvature of the interface. We discuss the variation of the average Gaussian curvature as a function of the surfactant volume fraction and its implication on the degree of local order of the bicontinuous structure. We also show a 3-D reconstructed morphology of the most disordered microemulsion.

Shear-flow-induced microstructural distortion of suspensions close to the critical point is described in detail on the basis of the Smoluchowski equation, where hydrodynamic interaction is neglected. The solution of the Smoluchowski equation exhibits scaling behaviour, predicting that the combined shear rate and correlation length dependence is characterized by a single dimensionless number λ ∼ γ ξ 4 (with γ the shear rate and ξ the correlation length of the unsheared suspension). From the scaling relations for deformation of the structure factor, a scaling form for the turbidity is derived. Experiments concerning these phenomena are presented, some of which are prelimanary. Two types of systems are used, both of which exhibit a gas-liquid critical point: stearyl silica in benzene and stearyl silica in cyclohexane with polydimethylsiloxane. Although there is an overall agreement with the theory, there remains a discrepancy in some of the quantitative comparisons, probably due to the neglect of hydrodynamic interaction and the approximate nature of the closure relation that is used for the three-particle correlation function.

The functional integral representation for the generating functional (GF) of the canonically averaged ensemble with an underlying Newtonian dynamics is obtained. It is shown that for this representation the non-linear fluctuation-dissipation theorem (NFDT) has the same form as for the Langevin dynamics case. This GF-representation is used for the investigation of the dynamics of the ϕ4-model with infinite range interactions at T > Tc. It is shown that the kinetic equation for the complete correlation function has the same form as for the Langevin dynamics case, which was considered before. All peculiarities of Newtonian dynamics are absorbed by one-particle (2-point and 4-point) correlator and response functions. The analysis of this equation shows that the 1/N-fluctuations (where N is the number of particles) restore the ergodicity of the system with the characteristicsrate τ−1 ∼ μ2/N, where μ is a coupling constant.

Exact results are obtained for the Ashkin-Teller model on a special Sierpinski carpet (SC). We calculate the partition function and correlation function with the transformation matrix method. Thus the asymptotic behaviour of the correlation function is investigated in the limit of long distance. The results show that no phase transition occurs at any finite temperature for the finite R (the order of ramification) fractal, which is consistent with the conclusion of the Ising and Potts model.